Decay and fission of oriented nuclei

The angular distributions of fragments originating from the binary decay of oriented spherical and deformed nuclei are investigated with allowance for correct transformation properties of wave functions under time inversion. It is shown that, as in the case of protonic decay, the adiabatic approximation for collective rotational degrees of freedom of the systems under investigation is inapplicable in describing the angular distributions of fragments of the deep-subbarrier alpha and cluster decays of nuclei. It is demonstrated that this approximation is justified in describing spontaneous and induced low-energy nuclear fission. The dependence of partial fission widths on the orientation of intrinsic axes, spins, and projections of spins and relative orbital angular momenta of fission fragments is analyzed by using the formalism of the unified theory of nuclear reactions and the theory of open Fermi systems. It is shown that the adiabatic approximation leads to the coherent interference between the wave functions for the relative motion of fragments, whereby the universal angular distributions of fission fragments of oriented nuclei is formed. Deviations from the A. Bohr formula are investigated for these distributions.     

Parity nonconservation in binary and ternary nuclear fission induced by polarized neutrons

Within the quantum-mechanical theory of the nuclear-fission process, the conditions of the emergence of coherent effects in the angular distributions of fragments originating from the binary and ternary fission of polarized nuclei are analyzed with allowance for the properties of transition fission states. In the case of ternary fission, the coefficients of P-odd asymmetry in the angular distributions of a light particle and a third particle, which is taken here to be an alpha particle, are calculated under the assumption that the third particle and two fragments are produced through a one-step mechanism. In order to confirm the ideas developed here, it is proposed to repeat, at a higher level of statistical accuracy, experiments devoted to seeking P-odd asymmetries for alpha particles in the ternary fission of nuclei.     

Angular distributions,relative orbital angular momenta,and spins of fragments originating from the binary fission of polarized nuclei

The angular distributions of fragments originating from the binary fission of odd and odd-odd nuclei capable of undergoing spontaneous fission that are polarized by a strong magnetic field at ultralow temperatures and from the low-energy photofission of even-even nuclei that is induced by dipole and quadrupole photons are investigated. It is shown that the deviations of these angular distributions from those that are obtained on the basis of the A. Bohr formula make it possible to estimate the maximum relative orbital angular momentum of fission fragments, this estimate providing important information about the relative orientation of the fragment spins. The angular distributions of fragments originating from subthreshold fission are analyzed for the case of the ²³⁸U nucleus. A comparison of the resulting angular distributions with their experimental counterparts leads to the conclusion that the maximum relative orbital angular momentum of binary-fission fragments exceeds 20, the fragment spins having predominantly a parallel orientation. The possibility is considered for performing an experiment aimed at measuring the angular distributions of fragments of the spontaneous fission of polarized nuclei in order to determine both the spins of such nuclei and the maximum values of the relative orbital angular momenta of fission fragments.     

Mechanisms of binary and ternary low-energy fission of nuclei with allowance for nonsphericity effects

Within the quantum-mechanical theory of fission, wave functions for fragments of binary nuclear fission and amplitudes of partial fission widths are constructed with allowance for a strong nonsphericity of fragment-interaction potentials. It is shown that, in the strong-coupling approximation, the symmetry axes of fission fragments are oriented along the symmetry axis of a fissile nucleus. The structure of the fragment-interaction potentials is analyzed, and the mechanism that is responsible for the alignment of the spins and relative orbital angular momenta of fission fragments and which explains the emergence of high fragment-spin values in experiments is substantiated. The mechanisms in question are generalized to the case of ternary nuclear fission. The fragment-interaction potentials and fragment wave functions are investigated, along with the partial fission widths with respect to the ternary fission of nuclei.     

Quantum description of quaternary nuclear fission

The quantum theory of binary and ternary fission is generalized to the case of recently observed quaternary nuclear fission. Formulas for the amplitudes of partial fission widths and angular and energy distributions of quaternary fission products are derived with allowance for strong channel coupling. The nonevaporation mechanism for formation of light particles is used to explain the experimentally observed decrease in the probability for emission of light particles (α, α), (α, t), and (t, t) as compared with the product of emission probabilities for the same particles in ternary fission. It is concluded that in quaternary fission, as in ternary fission, light particles escape from the neck of the fissioning nucleus much earlier than scission of the nucleus into heavy fragments occurs.     

Unified Mechanism behind the Appearance of <Emphasis Type="Italic">T</Emphasis>-Odd TRI and ROT Asymmetries in Actinide Fission Induced by Cold Polarized Neutrons

Some shortcomings of the approaches that are used to describe T-odd ROT and TRI asymmetries in true ternary fission via reactions involving the emission of prescission alpha particles and which are based on employing the classical method of trajectory calculations are analyzed. These shortcomings are caused by the disregard of the interference between the fission widths of different sJ_s neutron resonance states formed in the first well of the deformation potential of fissile compound nuclei. It is shown that the method used in some studies to determine T-odd TRI-asymmetries for prescission alpha particles is at odds with basic concepts of the generalizedmodel of the nucleus and approaches to constructing collective (for example, bending) vibrations of a fissile compound nucleus. Quantum-mechanical fission theory is generalized via employing a unified mechanism of formation of T-odd TRI and ROT asymmetries for prescission alpha particles and evaporated photons (neutrons). The proposed mechanism takes correctly into account the effect of quantum rotation of a fissile compound nucleus on the angular distributions of fission fragments and alpha particles for true ternary fission, as well as on the angular distribution of prompt photons (neutrons) emitted by fragments originating from the delayed fission of the aforementioned nuclei.     

Decisive role of wriggling vibrations in the formation of angular and spin distributions of products originating from binary and ternary fission of oriented nuclei

It is shown that the multiplicities and angular and energy distributions of neutrons and photons evaporated from thermalized fragments originating from the spontaneous and low-energy induced fission of nuclei, the relative yields of ground and isomeric states of final fragments, and the features of delayed neutrons emitted upon the beta decay of the above fragments can successfully be described by employing nonequilibrium distributions of spins and relative orbital angular momenta of fission fragments formed in the vicinity of the scission point for the fissile nucleus being studied. It is also shown that these distributions, which are characterized by large mean values of the spins and orbital angular momenta directed orthogonally to the symmetry axis of the fissioning nucleus are successfully constructed upon simultaneously taking into account zero-mode transverse wriggling and bending vibrations of a fissile compound nucleus in the vicinity of its scission point, the wriggling vibrations being dominant. It is confirmed that the zero-mode wriggling vibrations considered immediately above are directly involved in the formation of the angular distributions of fragments originating from the spontaneous and low-energy fission of nuclei. This makes it possible to describe successfully such distributions for photofission fragments.     

Angular momentum misalignment in deep inelastic processes and angular distribution of sequentially emitted particles and gamma rays

The angular momentum misalignment for fragments produced in deep inelastic scattering is discussed in terms of the thermal excitation of angular-momentum-bearing modes in the intermediate complex. Analytical expressions for the in- and out-of-plane angular distributions are obtained for sequentially emitted particles and fission fragments. The angular momentum dependence of the ratio between particle and neutron decay widths is explicitly treated and found to be quite important. Similarly angular distributions are obtained both for dipole and quadrupole gamma decay. The theoretical results are compared with experimental angular distributions of sequential fission fragments, sequential alphas and gamma rays, and a good agreement is found.     

Angular correlations in nuclear fission

Interference effects in the angular distributions of products originating from binary and ternary nuclear fission induced by slow neutrons are reviewed.     

Kinetic energy and angular distributions of instantaneous fission fragments in a classical model

The process of instantaneous fission in deep inelastic collisions is investigated in a classical model. Kinetic energies and angular distributions of the fragments are calculated for the proposed reaction Pb+U atE _cm ^inc =750 MeV; an experimental setup for the separation of the fragments originating from instantaneous fission from the fragments of thermal fission is explained. We also discuss fusion following instantaneous fission as a mechanism for the production of superheavy elements and arrive at rather promising estimates.     

Coaxial Fission of Nuclei to Three Commensurate Fragments

Trajectory calculations of the angular distribution of fragments originating from the spontaneous true ternary fission of ²⁵²Cf nuclei are performed with allowance for the rotation of the fissile-nucleus axis. This rotation arises upon scission because of the formation of fragment spins despite the conservation of zero total angular momentum at all fission stages. The calculations in question lead to the conclusion that a collinear tripartition is the most probable in spontaneous true ternary fission of ²⁵²Cf nuclei. This confirms experimental data, thereby creating the basis that is necessary for obtaining deeper insight into them.     

<Emphasis Type="Italic">P</Emphasis>-even correlations in binary and ternary nuclear fission induced by polarized neutrons

The evolution of a fissile nucleus from transition fission states specified at the saddle point of the deformation potential to fission states associated with prescission configurations of this nucleus and characterized by a pearlike shape of the nucleus is studied within the quantum-mechanical theory of fission processes that is based on the time-independent formalism. The coefficients of P-even asymmetries in the angular distributions of a light fragment and a third particle are calculated on the basis of the idea of the one-step mechanism of the production of a third particle and two fragments from the ternary fission of nuclei that is induced by polarized thermal neutrons. In order to confirm the developed concepts, it is proposed to repeat, at a higher level of statistical accuracy, experiments devoted to observing left-right asymmetries in the angular distributions of alpha particles from the ternary fission of nuclei.     

The quantum and thermodynamical characteristics of fission taking into account adiabatic and nonadiabatic modes of motion

In the framework of the quantum theory of spontaneous and low-energy induced fission, the nature of quantum and thermodynamical properties of a fissioning system is analyzed taking into account adiabatic and nonadiabatic modes of motion for different fission stages. It is shown that, owing to the influence of the Coriolis interaction, the states of the fissile nucleus and of primary fission products are cold and strongly nonequilibrium. The important role of superfluid and pairing nucleon-nucleon correlations for binary and ternary fission is demonstrated. The mechanism of pumping of high values of relative orbital momenta and spins of fission fragments for binary and ternary fission and the nonevaporation mechanism of formation of third particles for ternary fission are investigated. The anisotropies and P-odd, P-even, and T-odd asymmetries for angular distributions of fission products are analyzed. The text was submitted by the author in English.     

Angular momenta of fission fragments in the α-accompanied fission of 252Cf

For the first time, average angular momenta of the ternary fission fragments ^{100, 102}Zr, ¹⁰⁶Mo, ^{144, 146}Ba and ^{138, 140, 142}Xe from the α-accompanied fission of ²⁵²Cf were obtained from relative intensities of prompt γ-ray transitions with the use of the statistical model calculation. Average values of the angular momenta were compared with the corresponding values for the same fission fragments from the binary fission of ²⁵²Cf. Results indicate the presence of a decreasing trend in the average values of angular momenta induced in ternary fission fragments compared to the same binary fission fragments. On the average, the total angular momentum extracted for ternary fission fragments is ∼1.4 ℏ lower than in binary fission. Consequently, results indicate that the mechanism of the ternary α-particles emission may directly effect an induction of angular momenta of fission fragments, and possible scenarios of such mechanisms are discussed. Further, the dependence of the angular momenta of ¹⁰⁶Mo and ¹⁴⁰Xe on the number of emitted neutrons from correlated pairs of primary fragments was obtained also showing a decreasing dependence of average angular momenta with increasing number of emitted neutrons. Consequences are briefly discussed.     

Angular distributions of fragments originating from the spontaneous fission of oriented nuclei and problem of the conservation of the spin projection onto the symmetry axis of a fissile nucleus

The concept of transition fission states, which was successfully used to describe the angular distributions of fragments for the spontaneous and low-energy induced fission of axisymmetric nuclei, proves to be correct if the spin projection onto the symmetry axis of a fissile nucleus is an integral of the motion for the external region from the descent of the fissile nucleus from the external fission barrier to the scission point. Upon heating a fissile nucleus in this region to temperatures of T ≈ 1 MeV (this is predicted by many theoretical models of the fission process), the Coriolis interaction uniformly mixes the possible projections of the fissile-nucleus spin for the case of low spin values, this leading to the loss of memory about transition fission states in the asymptotic region where the angular distributions of fragments are formed. Within quantum-mechanical fission theory, which takes into account deviations from A. Bohr’s formula, the angular distributions of fragments are calculated for spontaneously fissile nuclei aligned by an external magnetic field at ultralow temperatures, and it is shown that an analysis of experimental angular distributions of fragments would make it possible to solve the problem of spin-projection conservation for fissile nuclei in the external region.     

Subthreshold photofission of even-even nuclei

Within quantum-mechanical fission theory, the angular distributions of fragments originating from the subthreshold photofission of the even-even nuclei ²³²Th, ²³⁴U, ²³⁶U, ²³⁸U, ²³⁸Pu, ²⁴⁰Pu, and ²⁴²Pu are analyzed for photon energies below 7 MeV. Special features of various fission channels are assessed under the assumption that the fission barrier has a two-humped shape. It is shown that the maximum value of the relative orbital angular momentum L _m of fission fragments can be found upon taking into account deviations from the predictions of A. Bohr’s formula for the angular distributions of fission fragments. The result is L _m ≈ 30. The existence of an “isomeric shelf” for the angular distributions of fragments from ²³⁶U and ²³⁸U photofission in the low-energy region is confirmed.     

Effects of rotation of fissioning nuclei in the angular distributions of prompt neutrons and gamma rays originating from the polarized-neutron-induced fission of 233U and 235U nuclei

The results of an experiment devoted to searches for effects of rotation of fissioning nuclei in the angular distributions of prompt neutrons and gamma rays originating from the polarized-neutron-induced fission of ²³³U nuclei are presented. The effects discovered in these angular distributions are opposite in sign to their counterparts in the polarized-neutron-induced fission of ²³⁵U nuclei. This is at odds with data on the relative signs of respective effects in the angular distribution of alpha particles from the ternary fission of the same nuclei and may be indicative of problems in the model currently used to describe the effect in question. The report on which this article is based was presented at the seminar held at the Institute of Theoretical and Experimental Physics and dedicated to the 90th anniversary of the birth of Yu.G. Abov, corresponding member of Russian Academy of Sciences, Editor in Chief of the journal Physics of Atomic Nuclei.     

Mechanisms of formation of P-odd,P-even and T-odd asymmetries in the angular distributions of products of binary and ternary fission induced by cold polarized neutrons

The experimentally measured P-odd, T-even; P-even, T-even; and P-even, T-odd asymmetries in the angular distributions of products of binary and ternary fission induced by cold polarized neutrons are classified, and the mechanisms of their appearance are studied. Basic asymmetries in the angular distributions of binary-fission fragments are found theoretically and are used to construct induced asymmetries in the angular distributions of prescission and evaporated third particles emitted in true and delayed ternary fission. If effects associated with the collective rotation of the polarized fissile system are disregarded, P-odd, T-even; P-even, T-even; and P-even, T-odd asymmetries in the angular distributions of prescission and evaporated photons are proven to be absent, and the coefficients of the analogous asymmetries in the angular distributions of prescission and evaporated neutrons are calculated for this case. The features of the coefficients of induced P-even, T-odd asymmetries are studied for evaporated photons and neutrons associated with taking into account the quantum rotation of the polarized fissile system.     

Mechanisms of excitation of <Emphasis Type="Italic">T</Emphasis>-odd correlations for prescission gamma rays and structure of these correlations

Conditions for the appearance and observation of prescission gamma rays emitted by a fissioning nucleus prior to its separation into fission fragments were investigated within quantum-mechanical fission theory. It is shown that these conditions are realizable in the gamma decay of isovector electric giant dipole resonances in a fissile nucleus that are excited because of nonadiabaticity of the collective deformation motion of the nucleus at the ultimate stages of its prefission evolution. Angular and energy distributions of prescission gamma rays emitted by unpolarized fissioning nuclei are analyzed. Features of T-odd correlations in angular distributions of gamma rays arising in the fission of unpolarized target nuclei that is induced by polarized cold neutrons are investigated, and it is shown that these correlations are similar in nature to T-odd ROT correlations discovered earlier for alpha particles emitted in the ternary fission of nuclei.